Onset of Flow-Induced Crystallization Kinetics of Highly Isotactic

Article pubs.acs.org/Macromolecules

Onset of Flow-Induced Crystallization Kinetics of Highly Isotactic Polypropylene Fawzi G. Hamad,† Ralph H. Colby,‡ and Scott T. Milner*,† †

Department of Chemical Engineering and ‡Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: Brief intervals of shear prior to a temperature quench accelerate crystallization, resulting in much smaller spherulites. Crystallization kinetics of five commercial linear isotactic polypropylenes were investigated, using a rheometer to impose shear and monitor crystallization after quenching. Shear and quench temperatures, shear rate, and duration were all systematically varied. The crystallization rate increases with increasing applied work, up to a value independent of undercooling beyond which the rate remains constant. This saturation is consistent with a maximum number of nuclei, possibly set by the concentration of heterogeneous impurities. The crystallization rate likewise increases with increasing shear rate, saturating at about 1 s−1 for all grades studied. Only chains in the high molecular weight tail, above about 104 kg/ mol, are stretched at this shear rate. Faster crystallization after shear was observed for grades with lower isotacticity. Flow-induced crystallization persists even when shear is applied well above the equilibrium melting temperature (187 °C), finally weakening above the Hoffman−Weeks temperature (210 °C), perhaps because flow-induced precursors are no longer metastable.

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INTRODUCTION When a semicrystalline polymer melt is subjected to deformation before a temperature quench, the rate of crystallization increases, and the solid polymer is found to contain smaller and more numerous spherulites or other semicrystalline structures.1−13 This flow-induced crystallization (FIC) has been widely studied, primarily in polypropylene, both because of its commercial importance and because the range of accessible crystallization rates are experimentally convenient. In commercial manufacturing processes, molten semicrystalline polymers are routinely subjected to large deformations just prior to crystallization. In injection molding, the molten polymer rapidly flows into a mold and experiences primarily shear flow as a result of the no-slip boundary conditions at the walls of the mold. In film blowing, molten polymer is forced through an annular die, which results in uniaxial extensional flow as the polymer flows through the contraction. Then, in the freestanding bubble above the die, the film is further drawn down in both the longitudinal and transverse directions, by the combined action of the processing line tension and the air pressure inside the bubble. The film thus is subjected to biaxial elongation.14 Generally speaking, these flows applied just prior to crystallization result in a higher number density of nuclei that grow into spherulites. The large number of nuclei leads to faster crystallization, as the growth rate of the nuclei is not strongly affected by the flow history. More nuclei result in smaller spherulites, which improve the final material properties relative to quiescent crystallization.1−7,15 © XXXX American Chemical Society

Previous work has identified important process parameters that govern the strength of flow-induced crystallization. These parameters are (1) the shearing temperature Ts, (2) the quench or crystallization temperature Tc, (3) the shear rate γ̇, and (4) the applied specific work W, defined as

W = σγ = ηγ 2̇ t

(1)

in which σ is the applied stress, γ the strain, η the shear viscosity at the applied shear rate, and t the duration of the applied shear. To assess whether the shearing temperature Ts and the crystallization temperature Tc are high, low, or intermediate, we begin by comparing them to the melting temperature Tm of crystallized polypropylene. For semicrystalline polymers that crystallize with a lamellar growth habit, the melting temperature Tm(h) depends on the lamellar thickness h; the lamellar thickness in turn is set by the crystallization conditions.16 Tm(h) is suppressed by the interfacial tension of the crystal−amorphous interfaces, leading to a 1/h correction given by the Gibbs−Thomson equation:

Tm = Tm° −

2σeTm° ΔHf h

(2)

In eq 2, ΔHf is the specific heat of fusion, σe is the interfacial tension of the crystal−amorphous interface, and Tm ° is the melting temperature of an infinitely thick crystal, i.e., the equilibrium melting temperature. By measuring Tm(h) for a Received: February 23, 2015 Revised: May 4, 2015

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DOI: 10.1021/acs.macromol.5b00386 Macromolecules XXXX, XXX, XXX−XXX

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oriented by the flow (τd(M)γ̇ = 1) and (b) chains just begin to be stretched by the flow (τR(M)γ̇ = 1) (see Figure 1).

range of samples with different lamellar thicknesses and fitting to the Gibbs−Thomson equation, Iijima and Strobl determined values for σe and the equilibrium melting temperature, which for isotactic polypropylene is 187 ± 2 °C.17 For polypropylene spherulites crystallized under typical conditions, whether quiescent or under flow, the melting temperature ranges from 160 to 170 °C. Using the Gibbs−Thomson relation, these values correspond to lamellar thickness from about 9−14 nm. As mentioned above, the lamellar thickness h is controlled by the crystallization temperature Tc; deeper quenches give smaller critical nuclei, resulting in thinner lamellae.16 Experimentally, the relation between Tc and h has the same general form as Tm(h); that is, Tc plotted versus 1/h also gives a straight line (the “crystallization line”), which lies below Tm(h) (the “melting line”), with a somewhat steeper slope.17 If the crystallization and melting lines are extended, they eventually cross at the Hoffman−Weeks temperature THW.18−20 For polypropylene, THW is around 208 ± 8 °C. Note that the crossing occurs for a negative (unphysical) value of 1/h. If this crossing occurred for a physical value of h, it would imply that smaller values of 1/h were inaccessible, since to produce them would require quenches so shallow that the resulting lamellae would be unstable to melting. Many authors have proposed that flow-induced crystallization results somehow from the effect of flow on aligning and stretching chains in the melt, which lowers the melt entropy and hence raises its free energy with respect to the crystal. The increased free energy difference at a given undercooling would lower the nucleation barrier, resulting in more nuclei, faster crystallization, and smaller spherulites.3,8,21−24 There is some evidence that FIC acts predominately on a small minority of long chains in a melt, rather than acting equally on the preponderance of chains in the sample.25−30 For a given deformation and molecular weight distribution, we can distinguish three groups of chains, based on how their stretch relaxation time (Rouse time) τR and orientational relaxation time (reptation time) τd compare to the deformation rate γ̇. We have (1) chains long enough to be stretched by the flow, with γ̇τR > 1; (2) chains too short to be stretched, but long enough to be oriented by the flow, with γ̇τR < 1 but γ̇τd > 1; and (3) chains too short even to be oriented by the flow, with γ̇τd < 1. Under the prevailing hypothesis, only chains in the first two groups can contribute to FIC, with the first group contributing most strongly.29,31,32 The Rouse time τR and reptation time τd are given by33,34

Figure 1. Schematic of the effect of shear on chains in the distribution. Chains with γ̇τd < 1 are undeformed, chains with γ̇τd ≥ 1 are oriented, and chains with γ̇τR ≥ 1 are stretched.

As the shear rate increases, the threshold molecular weights move leftward along the molecular weight axis, so that more of the chains in the high molecular weight tail are stretched by the flow and more of the chains in the bulk of the molecular weight distribution are oriented by the flow. Kimata et al. have shown that even though stretched high molecular weight chains are essential for FIC, these long chains are not overrepresented in flow-induced nuclei compared to the remaining of the sample.36 These claims were made by performing small-angle neutron scattering (SANS) experiments on polypropylene samples with deuterium-labeled chains of specific molecular weight. Samples were sheared using pressuredriven flow, applying a shear stress of 0.14 MPa for 1 s at 180C, followed by quenching to 140 °C. Results indicated that the concentration of deuterated long chains in flow-induced precursors matched the concentration in the material as a whole. It was concluded that as the long chains stretch and propagate to form precurors, they incorporate other chains in their vicinity. Nevertheless, long chains are still instrumental for FIC, since the stretching process is still dictated by them. It turns out that in most FIC experiments the shear rates are low enough that most chains are not stretched by the flow. In contrast, for well-entangled melts it is not difficult to access shear rates sufficiently large that most chains in the melt are oriented by the flow (this corresponds to a shear rate in the shear-thinning region of the viscosity versus shear rate flow curve).33 In this regime of shear rates, increasing the shear rate will increase the fraction of chains that are stretched by the flow and therefore should increase the strength of FIC, under the prevailing hypothesis. Studies have also shown that the enhancement of crystallization rate by flow is more pronounced for stretched chains with higher molecular weight.6,31,37 In the present work, we can check these implications of the prevailing hypothesis by comparing the strength of FIC effects for different commercial samples to the fraction of stretchable chains in the molecular weight distributions. The minimum shear rate (γ̇min) required for FIC is related to the inverse Rouse time of the longest chains in the molecular weight distribution.6,15,28 As the shear rate increases above the minimum inverse Rouse time, more nuclei form, and the crystallization rate increases.21,38 Winter et al. showed that for shear rates well below the inverse of the longest Rouse time

⎛ M ⎞2 τR = ⎜ ⎟ τe ⎝ Me ⎠ τd = 3

M τR Me

(3)

in which Me is the entanglement molecular weight and τe the Rouse time of an entanglement strand. These values are obtained by comparing experimental viscoelastic response to tube model predictions. For isotactic polypropylene at 170 °C, the corresponding values are Me = 5.25 kg/mol and τe = 1.5 × 10−7 s.35 (The above value for Me corresponds to the convention Ge = 4ρRT/(5Me) relating Me to the entanglement modulus Ge of the melt.) For a given deformation rate γ̇, the molecular weight distribution can be divided into three portions, separated by the threshold values of M at which (a) chains just begin to be B


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Macromolecules crystallization kinetics and final morphology are the same as for quiescent crystallization.38 No change in crystallization kinetics or morphology is expected when γ̇ < γ̇min, even if the shear is applied for a long time, since the chains can only be oriented but not stretched.39 Many authors have observed that as the applied work W is increased, crystallization after the quench is accelerated. It has been hypothesized that greater amounts of applied work causes stretched chains to aggregate and form more nuclei.28,39,40 Because greater specific work and greater undercooling both speed crystallization, several authors have asserted that they both decrease the nucleation barrier.4,8,22 Many authors have concluded that shear flow decreases the nucleation barrier by increasing the local alignment of chains.8,16,22,23,40 At first sight, applied work is a strange variable to quantify the amount of flow applied to a sample: why not simply the shearing time or total strain? Several authors provide evidence that specific work is a better variable than time or strain to characterize the amount of shearing in FIC. Baert et al. have shown that the effect of a given total strain on the crystallization rate is weaker at low shear rates than at higher shear rates.41 Janeschitz-Kriegl identified work as a controlling parameter by studying the relaxation time of flow-induced precursors to crystallization. He found that applying low stress for a long time produces similar precursors as applying high stress for a short time.42 Many authors have observed a threshold “critical work” Wc for flow-induced crystallization. Above Wc, the crystalline morphology changes from spherulites to an anisotropic structure aligned with the flow. Janeschitz-Kriegl et al. observed that when W exceeds Wc, the number density of nuclei no longer depends on crystallization temperature and the morphology transitions to a highly oriented structure.4,8,9,23,40,43 They speculate that as the amount of applied work increases, nuclei become longer and the fraction of chains that are aggregated becomes larger, which eventually causes the formation of thread-like nuclei. Meijer et al. observed that after applying a certain amount of specific work, the crystallization rate saturates and becomes constant thereafter.3 However, a second region of accelerated crystallization rate was observed when increasing specific work further after saturation. They assert that the first and second increases in crystallization rate are driven by two distinct behaviors, corresponding to an increase in nuclei number density and a change in crystalline morphology, respectively. Therefore, the work at which this second transition occurs is Wc. In an early study, Lagasse and Maxwell showed that the onset of observable flow-induced crystallization is affected by the addition of nucleating agents, which speed up crystallization under quiescent conditions.6 For samples with nucleating agents added, the apparent onset of FIC with increasing applied work is delayed, until the rate of flow-induced nucleation is high enough to be comparable to the enhanced nucleation rate caused by the nucleating agents. Ryan et al. identified the critical work threshold by shearing polyethylene between two parallel plates; this geometry gives shear rate and applied work that vary radially in the sample, increasing from the center outward. Crystallized samples imaged with crossed polarizers show a radial boundary between unaligned and aligned material, corresponding to the critical work threshold.28,39,44 They found that the critical work is constant over a wide range of shear rates; however, below a

critical shear rate, the specific work required to form oriented structures increases with decreasing shear rate.39 Since the critical shear rate is associated with the relaxation time of the longer polymer chains in the distribution, they believe that as the population of these chains decreases, the amount of work needed to form anisotropic structures increases. In the present work, we investigate flow-induced crystallization of linear isotactic polypropylene for a variety of commercial grades, with different molecular weight distributions and degrees of isotacticity, in order to determine how the strength of FIC effects varies with material characteristics. We focus on the effects on the crystallization rate of the four key processing parametersshear rate, applied work, crystallization temperature Tc, and shearing temperature Tsall of which are in principle adjustable in commercial manufacturing processes.

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EXPERIMENTAL SECTION

All rheological measurements were performed using a Rheometrics ARES-LS rheometer, using a 25 mm cone (5.7 angle and 0.048 mm truncation gap) and plate fixtures and a nitrogen blanket to help prevent sample oxidation. Samples for the rheometer were prepared by press-molding polypropylene into disks of 25 mm diameter and about 1 mm thickness, at 200 °C for about 30 min under vacuum. Linear Viscoelasticity. Linear viscoelastic response of polypropylene materials were determined using oscillatory rheology, with frequencies ranging from 0.1 (0.001 for the highest temperature) to 100 rad/s, and temperatures ranging from 150 to 230 °C. Master curves of the dynamic moduli G′(ω) and G″(ω) spanning nearly 5 decades in frequency were constructed using time−temperature superposition. The temperature range (150−230 °C) was limited at the low end to avoid crystallization and at the high end to prevent sample degradation. Strain amplitudes were increased for measurements at low frequencies to maintain measurable stress levels, while making sure to remain in the linear regime. Quiescent Crystallization. To erase any remaining memory of sample preparation (from pellet extrusion or molding disks for the rheometer) samples were annealed in the rheometer at 220 °C (well above the equilibrium melting temperature) for approximately 10 min prior to rheological measurements. The sample was then cooled to 170 °C, just above the melting temperature of typical iPP spherulites. After the temperature equilibrated, an oscillatory time sweep was initiated (at constant frequency of 0.5 rad/s and strain amplitude of 0.05). The sample was then quenched to the desired crystallization temperature, at a cooling rate of about 15 °C/min. To detect the onset of crystallization, the viscoelastic response at a constant frequency ω0 was monitored as a function of time, following the methods developed by Pogodina and Winter.10 For the commercial iPP grades studied, the frequency ω0 = 0.5 rad/s falls in the middle of the crossover to terminal behavior, where G′(ω) and G″(ω) are comparable, but the viscous response still dominates. As the sample crystallizes, a tenuous network of connected crystallites develops, which imparts an elastic modulus to the sample. This growing elastic modulus shifts the phase angle tan δ = G″(ω0)/G′(ω0). The threshold value tan δ = 1, identified by ref 10 as a convenient indicator of an “incipient gel”, was chosen to determine the “crystallization time”.7,10,45,46 More precisely, the gelation time is identified as the time required for tan δ to become independent of frequency,7,10 found by performing a series of frequency sweep tests on a slowly crystallizing sample. We have verified that the gelation time so defined is consistent with our tan δ = 1 definition of crystallization time. The strain amplitude of 0.05 for monitoring crystallization was chosen to provide sufficient signal without affecting crystal growth. Linear response was verified by strain amplitude sweeps. The most strain-sensitive state is the incipient gel (tan δ = 1). We have verified explicitly that duplicate measurements with strain amplitudes of 0.02 and 0.05 give equivalent results, while larger strain amplitudes can significantly delay the time to reach tan δ = 1. C


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Macromolecules Flow-Induced Crystallization. To investigate flow-induced crystallization in a controlled manner, we make use of a shearing and cooling protocol similar to those used in previous studies.11,22,29,39 In essence, our protocol is the same as for the quiescent crystallization studies described above, with the addition of an interval of steady shear applied after the annealing step, just before the quench (see Figure 2).

°C crystallization is so rapid that it begins before the quench is complete. Linear Viscoelastic Modeling. Small amounts of long-chain branching have been hypothesized to have substantial effects on flowinduced crystallization.47 Because of the nature of the catalysts used in their synthesis, the commercial iPP grades studied here should consist exclusively of polydisperse linear chains, with no long-chain branching. By far the most sensitive way to detect low levels of long-chain branching is by their effect on melt rheology. Modeling the linear viscoelasticity of polydisperse branched melts remains a challenging problem, in particular because of the need to specify the ensemble of branched structures in the melt. In contrast, modeling the linear viscoelasticity of well entangled melts of polydisperse linear chains is largely a solved problem. To verify that our samples do not contain detectable levels of longchain branching, we compared the observed linear viscoelastic response to tube model calculations for a melt of linear iPP chains with the observed molecular weight distribution. The calculations of the linear viscoelastic response were performed using the BoB (branch on branch) program, developed by D. Read and C. Das at the University of Leeds.48 For polydisperse linear chains, BoB takes as input the entanglement molecular weight Me, entanglement strand Rouse time τe, monomer molecular weight, melt density, and the molecular weight distribution. The molecular weight distribution can be input to BoB as one of several common functional forms (e.g., most probable, log-normal, Gaussian) or as a list of monodisperse components and corresponding weight fractions. In the present work, we represent the molecular weight distribution as a large number of monodisperse components, chosen to fit the shape of the cumulative mass distribution versus log molecular weight. An example of this representation (for sample CiPP1) is shown in Figure 3. In the figure, the smooth curve is the

Figure 2. Shear-temperature protocol applied to a polymer melt during a flow-induced crystallization experiment. Temperature profile (blue line) and shear rate (red line) on a common time axis. Protocol consists of (1) annealing the melt at 220 °C, (2) shearing at Ts, and (3) quenching to the crystallization temperature Tc. As for quiescent crystallization studies, we anneal the sample at 220 °C for 10 min, followed by cooling to the shearing temperature Ts (170 °C unless otherwise specified). After the temperature equilibrates at Ts, the sample is sheared at a specified constant shear rate for a certain amount of time. The stress overshoot for all experiments occurs within 1 s of the onset of shear, whereas the shearing times ranged from 7 to 4000 s; hence, the shearing extends well beyond the stress overshoot in all our experiments. After shearing is complete, we proceed as for the quiescent crystallization studies; an oscillatory time sweep is initiated at a constant frequency of 0.5 rad/s and strain amplitude of 0.05, and the sample is quenched to the crystallization temperature Tc (141 °C unless otherwise specified). The cooling rate used was ∼15 °C/min; however, in order to avoid the temperature undershooting, the cooling rate was gradually lowered as we approached the desired crystallization temperature. The total time required to cool from Ts to an equilibrated Tc was approximately 5 min. The linear viscoelastic response at ω0 = 0.5 rad/s as a function of time is used to monitor the crystallization. Table 1 summarizes the shear rate, specific work, and temperature ranges that have been investigated in this study. Note that we studied a

Table 1. Range of Shear Rates, Specific Work, Shearing Times, and Temperatures Applied to Polypropylene Melts in Our Experiments variable

range

shear rate [s−1] work [MPa] shearing time [s] shear temperature Ts [°C] crystallization temperature Tc [°C]

0.52−90 1−35 7−4000 160−240 130−142

Figure 3. Measured cumulative mass fraction versus log molecular weight for sample CiPP1 (smooth curve) and representation as a sum of monodisperse components (stairstep curve) used for BoB predictions. integral of the measured mass distribution, and the “stairstep” curve is the representation in terms of monodisperse components. In practice, the stairstep cumulative distribution molecular weights and mass fractions may either be fitted to minimize the mean-square distance between the two cumulative distributions or simply adjusted by hand with a large enough number of components to give a close match to the measured cumulative mass distribution. Figure 4 shows experimental results for G′(ω) and G″(ω) for all five commercial samples studied here compared to BoB calculations of the linear viscoelastic response. The agreement between observed and predicted viscoelastic response through the entire terminal region, with

range of shearing temperatures, from 240 down to 160 °C. We avoided Ts < 160 °C because at such low temperatures the samples crystallize appreciably during the shear, complicating the experiment and its interpretation. Likewise, we studied a range of crystallization temperatures Tc from 142 down to 130 °C. Above 142 °C, crystallization takes an inconveniently long time, while below 130 D


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Figure 4. Master curves for five commercial iPP grades at reference temperature 170 °C for (a) G′ and (b) G″. Solid curves are tube model predictions using BoB (see main text).

Table 2. Physical Properties of the Five IPP Grades grade

MW [kg/mol]

MW/MN

CiPP1 CiPP2 CiPP3 CiPP4 CiPP5

448 158 236 462 474

7.2 3.7 6.0 8.6 5.7

[mm] 93.4 98.3 95.4 96.7 95.1

± ± ± ± ±

[mr] + [rm]

0.5 1.0 0.9 0.8 0.5

4.6 1.4 3.4 1.8 2.1

± ± ± ± ±

0.3 0.6 0.5 0.4 0.2

[rr] 1.9 0.4 1.1 1.5 2.8

± ± ± ± ±

0.3 0.4 0.4 0.4 0.2

[m] (tacticity) 95.7 98.9 97.1 97.6 96.2

± ± ± ± ±

0.5 1.0 0.9 0.8 0.4

Figure 5. (a) Molecular weight distribution of all five grades. (b) Closeup of the high molecular weight tails. Curves: 1 → CiPP1, 2 → CiPP2, 3 → CiPP3, 4 → CiPP4, and 5 → CiPP5. no spurious elastic response at low frequencies not predicted by the assumption of linear chains, is strong evidence that our samples do not contain long-chain branching. 13 C NMR. The tacticity of the commercial polypropylene samples was obtained by 13C NMR. Before preparing samples for NMR, antioxidants and other trace impurities that could potentially contaminate the NMR signal were removed as follows. Polymer was dissolved at 2 wt % in 1,2,4 trichlorobenzene at 180 °C (well above Tm) for 5 h under an argon blanket to protect against oxidation. The solution was precipitated in a 6-fold excess of room temperature acetone and then filtered. This dissolution and precipitation process was repeated, whereupon the purified polypropylene was dried in a vacuum oven. NMR samples were prepared by dissolving the purified polypropylene in 1,1,2,2-tetrachloroethane-d2 in a vacuum oven for 2 h. 13 C NMR was carried out using a Bruker AM-300 instrument, with the sample held at 110 °C. Data were acquired for 13−15 h to improve the signal-to-noise ratio. 13 C NMR can be used to characterize the stereochemical placement of adjacent monomers along an iPP chain and so determine its tacticity. A meso placement (m) consists of two adjacent monomers stereochemically oriented in the same direction; a racemic placement

(r) is two adjacent repeat units oriented oppositely. The tacticity is the probability [m] of a meso bond between adjacent monomers. From the integrals of chemically shifted NMR peaks corresponding to the methyl carbon, one can determine the probabilities of the three possible stereochemical triads: isotactic (mm), heterotactic (rm or mr), and syndiotactic (rr), with corresponding probabilities [mm], [rm] + [mr], and [rr]. (By symmetry, [rm] equals [mr].) The tacticity is determined from the triad probabilities as follows: [m] = [mm] + [mr ]

(4)

expressing the fact that m must be followed by either m or r. Tacticity percentages obtained for the five grades are summarized in Table 2; these values give the percent of repeat units that are isotactic. The errors in [mm], [rm] + [mr], and [rr] are calculated by integrating the noise of the baseline over the width of their respective triad peak. The baseline was repeatedly integrated over a wide range, resulting in a series of values that have normal distribution with the mean at zero. Error bars were calculated using the variance of this distribution. E


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has been suggested to contribute strongly to flow-induced crystallization. The linear viscoelastic data can be usefully presented in another form, as plots of the magnitude |η*(ω)| of the complex viscosity, shown in Figure 6. (The complex viscosity η*(ω) is

RESULTS AND DISCUSSION In this work, our goal is to discover what attributes of semicrystalline polymer samples influence the strength of flowinduced crystallization, and the range of processing parameters over which flow-induced crystallization occurs, by comparing the behavior of a suite of commercial isotactic polypropylenes. To this end, we examined five different grades of commercial isotactic polypropylene (CiPP). Key characterization attributes of these grades are summarized in Table 2. Sample Characteristics. From Table 2, we see that all five grades are highly isotactic, with tacticity (percent meso addition of successive monomers) varying from 95.7 up to 98.9. The samples vary in weight-average molecular weight MW from 158 up to 474 kg/mol, and all are significantly polydisperse, with MW/MN ranging from 3.7 up to 8.6. All commercial polypropylene homopolymers are known to have been produced in a slurry polymerization process using a Ziegler− Natta catalyst. Figure 5 provides a more detailed look at the molecular weight distribution, obtained from size-exclusion chromatography. The molecular weight distributions are all unimodal, roughly similar in shape. Of particular interest are the high molecular weight tails for each sample (Figure 5b), since the prevailing hypothesis for the mechanism of flow-induced crystallization suggests that chains long enough to be stretched by the flow contribute most strongly to enhanced nucleation. The five grades can be rank-ordered with respect to the prominence of their high molecular weight tails: CiPP2 has the weakest tail, followed by CiPP3, with CiPP1, CiPP4, and CiPP5 roughly comparable. Another more detailed characterization tool, particularly important for flow-induced crystallization studies, is linear viscoelasticity. Figure 4 shows dynamic rheology data for all five grades. The data were obtained over a range of temperature 140−230 °C and a range of frequencies 0.1−100 rad/s (down to 0.001 rad/s for the highest temperature) and shifted to a master curve at a reference temperature of 170 °C using time− temperature superposition. From the temperature-dependent shift factors, the activation energy of all grades was found to be about 42 kJ/mol, consistent with previously reported values for isotactic polypropylene.49,50 The different grades show a range of viscoelastic responses, with each grade reaching terminal response at a different frequency. CiPP2 and CiPP5, with lowest and highest average molecular weight, are fastest and slowest to relax, respectively. The solid curves in Figure 4 are tube model predictions of the viscoelastic response computed using the program BoB (branch on branch), from the measured molecular weight distributions and the assumption that all chains are linear.48 The same values of entanglement molecular weight Me = 5.25 kg/mol and entanglement strand Rouse time τe = 1.5 × 10−7 s were used in the predictions for all grades, with the exception of CiPP5. A slightly larger τe = 2.5 × 10−7 s was used for CiPP5 in order to correctly predict the experimental LVE data. It is not clear what induces this increase in τe for CiPP5; there is nothing in our extensive characterization that suggests difference of this sort. The experimental dynamic response is in good agreement with BoB predictions for all grades; we observe no anomalous low-frequency elastic response, which is a sensitive indication of low levels of long-chain branching. By this comparison, we can attest that our samples do not contain rheologically detectable levels of long-chain branching, which

Figure 6. Complex viscosity of five commercial iPP grades at reference temperature 170 °C.

defined in terms of the complex modulus G*(ω) by −iωη*(ω) = G*(ω).) According to the Cox−Merz rule, the shape of |η*(ω) | is very similar to the “shear-thinning curve” of steady shear viscosity η(γ̇) versus shear rate.51 The Cox−Merz rule is well obeyed by smoothly polydisperse linear entangled melts.52 The curve |η*(ω)| highlights the onset of shear thinning, which occurs at lower frequencies for the more slowly relaxing samples. Crystallization Monitoring. After a protocol of annealing, shearing, and quenching a sample in the rheometer, the crystallization kinetics are observed by monitoring the linear viscoelastic response at a single frequency as a function of time. The details of this technique, developed by refs 7 and 11, are presented in the Experimental Section. Typical results are shown in Figure 8. These particular experiments were performed on CiPP1, with a shear rate of 2.5 s−1 at 170 °C and applied specific work of (a) 4.1 MPa and (b) 25.4 MPa. In Figure 8a, the initial increase in modulus over the first 2 min is due to the decrease in temperature on quenching from Ts to Tc (here, from 170 to 141 °C). After the crystallization temperature is reached (at about t = 3 min), both G′ and G″ remain constant until the sample crystallizes sufficiently that the elastic modulus begins to climb (starting at about t = 20 min in Figure 8a). The increase in elastic modulus is a consequence of crystalline lamellae growing outward from the nuclei during crystallization. Eventually these lamellae reach a percolation threshold (gel point), at which they span the entire sample to form a network of interconnected spherulites, causing the modulus to grow rapidly. As crystallization progresses, the interconnections increase, transforming the sample rheology from viscous to elastic. G′ overtakes G″ (hence tan δ = 1) at about t = 60 min in Figure 8a. To confirm this scenario, we have taken optical micrographs of a thin slice from an FIC sample subjected to 5 MPa of applied work, melted, and recrystallized with the same cooling protocol as in the rheometer. (In separate experiments to be published, we show that the recrystallization kinetics of FIC samples that have been melted but not extensively annealed is F


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Macromolecules nearly identical to the kinetics of the first crystallization.) The microscopy image in Figure 7 shows that after 60 min at 141 °C (at which time we would reach tan δ = 1 in an FIC experiment at 5 MPa) the spherulites form a connected network across the sample.

unsheared sample. The extent of edge fracture increases with shear rate and applied work, as is evident in comparing Figure 8a to Figure 8b; much more work was applied in (b), much more sample escaped, and G′ and G″ for the sheared sample are more dramatically shifted downward. However, the phase angle tan δ is insensitive to escape of a portion of the sample because it only measures the phase relation between the applied strain and the measured stress or equivalently the ratio of the in-phase and out-of-phase stress response. Consequently, tan δ provides a useful way to detect crystallization; the time to reach tan δ = 1 is a good practical measure of crystallization time,7,11 with good reproducibility in duplicate experiments. Quiescent Crystallization. Many aspects of quiescent crystallization have been extensively studied and are well understood. A central feature of quiescent crystallization is that greater undercooling decreases the activation barrier for nucleation, which leads to a greater concentration of nuclei and hence faster crystallization.16,22,54,55 The quiescent crystallization time for a sample at a given crystallization temperature Tc serves as the reference point for flow-induced crystallization experiments. We have carried out quiescent crystallization experiments on our five commercial iPP grades as a function of crystallization temperature Tc, from 142 °C down to 130 °C. This temperature range was selected because quiescent crystallization above 142 °C takes many hours, while for Tc below 130 °C crystallization progresses before the quench is completed. Figure 9 presents our quiescent crystallization results (about four repeats), in which the crystallization time has been taken as the time to reach tan δ = 1 as described in the previous section. Generally speaking, all our samples show similar crystallization times versus Tc, ranging from about 500 min at Tc = 143C down to about 10 min at Tc = 130 °C. A closer examination reveals substantial differences between the different samples, with CiPP2 and CiPP3 crystallizing more quickly, followed by CiPP4, and with CiPP1 and CiPP5 crystallizing more slowly. In quiescent crystallization, polymers with higher molecular weight and lower isotacticity have been shown to crystallize more slowly.27,56 Longer chains in the melt have lower mobility and consequently have a lower crystalline growth rate. Lower tacticity chains have shorter isotactic sequences, separated by

Figure 7. Polarized optical micrograph of sheared CiPP1 (γ̇ = 2.51 s−1 and W = 5 MPa), melted at 170 °C, cooled to 141 °C, and recrystallized for 60 min (equal to the time to tan δ = 1 in FIC rheometer experiments at W = 5 MPa). Scale bar = 500 μm.

The range of shear rates used during the steady shear portion of our protocol can cause secondary flows, which result in some of the sample escaping out of the gap between the cone and plate fixtures, a phenomenon known as edge fracture.53 The escape of a portion of the sample leads to a lower measured stress and thus an apparent decrease in moduli. This effect is visible in comparing the time-dependent values for G′(ω0) and G″(ω0) of a sample that has been sheared (square symbols in Figure 8) to the values for a sample that has not been sheared (star symbols on the vertical axis). The values of G′ and G″ for the sheared sample are shifted downward with respect to the

Figure 8. Time sweep at ω = 0.5 rad/s and γ0 = 0.05 to monitor crystallization. (a) CiPP1, with γ̇ = 2.5 s−1 and W = 4.1 MPa. (b) CiPP1, with γ̇ = 2.5 s−1 and W = 25.4 MPa. Shearing temperature Ts = 170 °C and crystallization temperature Tc = 141 °C in both (a) and (b). G′ (filled square), G″(open square), and tan δ (open triangle). Unsheared values of G′ (filled star) and G″ (open star) are shown for reference. G


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clearly visible in the data for CiPP1), with a smaller slope between about 134 and 138 °C than above or below this range. This behavior may reflect different regimes in the mechanism for the growth of crystalline lamellae. Hoffman described three regimes of lamellar growth (called regimes I, II, and III), each corresponding to a different mechanism for the addition of new chain stems to the edge of a growing lamella.59−62 The transitions between regimes have been reported to occur at 153 °C (I to II) and 137 °C (II to III).60,63 The mechanisms differ with respect to the process of “secondary nucleation”, under which a new chain stem is added to a completed layer of stems on the growth face; addition of stems next to an existing stem or partial layer is more rapid than addition of the first stem to a flat face. At small undercoolings (regime I, Tc > 153 °C), the barrier to adding the first stem is large enough that secondary nucleation is rare on the growing face. In regime II (137 °C < Tc < 153 °C), multiple secondary nucleation begins to be prevalent. In regime III (Tc < 137 °C), secondary nucleation is so facile that the growing interface becomes rough.63 Finally, note that all our commercial polypropylene samples undergo heterogeneous primary nucleation, in which the nucleation barrier is lowered by the presence of impurities or small particles. In careful experiments to observe homogeneous nucleation in isotactic polypropylene, using samples purified by crystallization from solution, homogeneous nucleation is observed on experimental time scales (minutes to hours) only at much greater undercoolings (Tc in the range 80−85 °C) than we reach in our experiments.64,65 In contrast, for unpurified commercial isotactic polypropylene, nucleation is readily observed on experimental time scales at much higher temperatures (Tc in the range 115−150 °C),66,67 as in our own observations of quiescent nucleation. Our samples contain a small, unknown quantity of particulate impurities, certainly including catalyst and support fragments, which are not separated from the polymer in commercial processes. These act as heterogeneous nucleation sites when a sample is quenched, lowering the surface free energy of the critical nucleus.65,68,69 Flow-Induced Crystallization. The goal of studying polypropylene grades with different properties (molecular weight and isotacticity) is to understand the influence of those properties on flow-induced crystallization. A key element of the prevailing view of flow-induced crystallization is that

Figure 9. Quiescent crystallization time for different grades versus crystallization temperature Tc.

segments with “stereo errors” (switching of the methyl group from one side of the chain to the other). These stereo errors are rejected from the crystals, much as comonomers are rejected. The entropic cost of rejecting stereo errors from a critical nucleus increases the nucleation barrier and hence the crystallization time. The final crystallinity of solid polymer is likewise reduced because some isotactic sequences are too short to incorporate in the crystalline lamellae.57,58 The differences in crystallization time between our various samples appear to arise from differences in their tacticity and molecular weight. On the basis of the above discussion, we expect the grades with the highest tacticity and lowest molecular weight will crystallize the fastest. Consulting Table 2, we find that the highest tacticity sample is CiPP2, followed in order by CiPP4, CiPP3, CiPP5, and finally CiPP1. We note also that CiPP2 has the lowest MW, followed by CiPP3, and CiPP1, CiPP4, and CiPP5 all with substantially higher MW. Thus, a good overall agreement is found between the order of crystallization times in Figure 9 and the values in Table 2, where CiPP2 (with the highest tacticity and lowest MW) crystallizes the fastest, followed by CiPP3 (with low MW and intermediate tacticity), then CiPP4 (with high tacticity but high MW), and finally CiPP1 and CiPP5 (both with low tacticity and high MW). In Figure 9, the overall trend of shorter crystallization time at lower Tc values appears to be broken into three regimes (most

Figure 10. Crystallization time versus shear rate, at fixed applied work (see legend). All samples sheared at 170 °C and crystallized at 141 °C. (a) Four of five grades show FIC behavior. (b) Crystallization time for CiPP2 is essentially independent of shear rate up to 90 s−1. H


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Macromolecules chains long enough to stretch in the flow will contribute most strongly to enhanced nucleation. For the range of shear rates used in our experiments, only chains in the high molecular weight tail of the molecular weight distribution have stretch relaxation times τR such that γ̇τR exceeds unity. From Figure 5, CiPP1, CiPP4, and CiPP5 have equally large high molecular weight tails, followed by CiPP3, with CiPP2 having the smallest high molecular weight tail. Thus, we might expect that CiPP1, CiPP4, and CiPP5 should show the strongest flow-induced crystallization response, followed by CiPP3, with CiPP2 having the weakest effect. To test these expectations, we performed flow-induced crystallization experiments using the shearing and quenching protocol described in the Experimental Section. As for the quiescent crystallization experiments, time-dependent linear viscoelasticity at a fixed frequency was used to monitor crystallization, with the crystallization time defined as the time at which tan δ = 1. Figure 10 shows results for FIC experiments carried out as a function of applied shear rate, with specific work held constant, at a shearing temperature of 170 °C and a crystallization temperature of 141 °C. Approximately 20 MPa of specific work was applied to all grades, with the exception of CiPP1 (12.5 and 25 MPa). Dependence on Shear Rate. For four of our five samples, the crystallization time rapidly decreases with increasing shear rate, by a factor of about 5−30 depending on the particular material, and then becomes constant at a saturation shear rate γ̇sat of about 1−2 s−1. One sample (CiPP2) shows essentially no change in the crystallization time, even at shear rates as high as 90 s−1. From Figure 6, we see that all of our samples are shear thinning over the range of shear rates applied in our FIC experiments; hence, typical chains in all samples are to some extent oriented in the flow. The onset of shear thinning is delayed in CiPP2 because of its lower molecular weight; however, for this sample we applied shear rates up to 90 s−1, well into the shear-thinning range for this material, without observing FIC. Some aspects of these results agree with our expectations based on the amount of high molecular weight tail in the distributions for the various grades: CiPP2 (with the smallest high molecular weight tail) shows no FIC effect, CiPP3 (with the next smallest tail) shows weak FIC, and CiPP1, CiPP4, and CiPP5 show the strongest FIC effect. However, CiPP1, CiPP4, and CIPP5 have essentially the same high molecular weight tail but show markedly different flow-induced crystallization, with CiPP1 exhibiting a much stronger response than the other two grades. These variations suggest that some other material property in addition to the high molecular weight tail also influences FIC. The decrease in crystallization time for shear rates between 0 and 1 s−1 is generally consistent with the hypothesis that chains stretched in the flow contribute strongly to FIC. As the shear rate increases, the minimum molecular weight M*(γ̇) for a chain to be stretched decreases, so that more of the high molecular weight tail can be stretched by the flow, presumably leading to a stronger FIC effect. This minimum molecular weight is given by the condition τR(M*) = γ̇−1, which implies that M* scales as γ̇−1/2. Using eq 3, a shear rate of 1 s−1 corresponds to a molecular weight M* = 1.4 × 104kg/mol, just at the edge of the high molecular weight tail. One qualitative feature of Figure 10 not evidently explained by the hypothesis that stretchable chains contribute strongly to FIC is the appearance of a saturation shear rate γ̇sat. From

Figure 10, we see that for CiPP1 at two different values of applied work (12.5 and 25 MPa), although the crystallization is more rapid for larger applied work, the saturation shear rate is the same. Indeed, all four samples seem to show the same saturation shear rate: shearing faster than 1−2 s−1 has no further effect on the crystallization time, even though there are many more slightly shorter chains in the high molecular weight tail that could have been stretched by a faster shear rate. This observation suggests that for some reason chains below a minimum molecular weight of about 104 kg/mol are not effective in initiating FIC. A minimum molecular weight requirement would also be consistent with the observation that CiPP2 does not display flow-induced crystallization at any shear rate (Figure 10b); for CiPP2, the high molecular weight tail does not reach 104 kg/mol (see Figure 5). Evidently, at a shear rate of 1 s−1 only a small minority of the chains in any of our samples are long enough to be stretched by the flow. The fraction of stretchable chains can be computed by integrating the molecular weight distribution from M* upward. We may ask whether the stretchable chains are sufficiently concentrated to overlap.70,71 We define overlap by the condition that the sum of the pervaded volumes for all the stretchable chains equals the system volume. The pervaded volume Ω(M) for a chain of mass M is given by Ω(M ) = (4π /3)R g(M )3

(5)

in which Rg is the radius of gyration, given by ⟨Rg2⟩ = b2M/ (6M0). At overlap the pervaded volume fraction becomes unity. The pervaded volume fraction ϕ can be written as an integral over the molecular weight distribution: ϕ=

4πb3ρNA 18 6 M 0

∞

∫log M* (M /M0)1/2 P( log M) d log M

(6)

In eq 6, b is the statistical segment length, ρ is the melt density, M0 is the monomer molar mass, and NA is Avogadro’s number. To derive eq 6, observe that the pervaded volume Ωi of chain i is given by Ωi = (4π/3)Rg,i3, in terms of its gyration radius Rg,i = (M/Mm)b2/6, where Mm is the mass of a monomer. The sum Vp of the pervaded volumes (assumed nonoverlapping) can be written Vp = 4πb3/(18√6)∑i(Mi/Mm)3/2. The sum over chains ∑i can be replaced by an integral over the number distribution PN(M), as ∑i → N ∫ dM PN(m), where N is the total number of chains. The number distribution is related to the mass distribution P(M), by MPN(M) dM = ρV/NP(M) dM, where V is the system volume. The pervaded volume fraction ϕ equals Vp/V, which can be rearranged to give eq 6. Figure 11 shows the pervaded volume fraction ϕ versus log M* for CiPP1, with the range of M* corresponding to a range of shear rates 0.53−2.5 s−1. Even at a shear rate of 2.5 s−1, the stretchable chains in CiPP1 are far below overlap, yet CiPP1 shows a strong flow-induced crystallization effect. This behavior suggests that overlap of stretchable chains in the melt is not an essential element of the FIC mechanism. Dependence on Specific Work. Applied specific work has long been identified as the second key flow parameter governing the strength of flow-induced crystallization.22,28,39,42,44 Generally speaking, increasing applied work leads to faster crystallization, in a manner qualitatively similar to increased undercooling. This is evident in Figure 10, where for I


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Figure 11. Pervaded volume fraction of stretchable chains in CiPP1 versus M* (bottom x-axis) and applied shear rate corresponding to inverse Rouse time of stretched chain (top x-axis). Figure 12. Crystallization time versus applied work, with shearing temperature 170 °C and crystallization temperature 141 °C. Shear rates for different grades (see legend) were chosen to be above γ̇sat for that grade.

CiPP1 we have presented data for two different applied work values (12.5 and 25 MPa). Although most authors now agree that specific work appears to be the proper way to measure the “amount of strain applied” in flow-induced crystallization experiments, some previous works have used total applied strain instead, in describing how shearing time influences flow-induced crystallization. To investigate which is a more appropriate control variable, we performed experiments in which the applied strain was varied while the specific work was held constant (by reducing the shear rate). We found that the magnitude of FIC effects were approximately strain independent at fixed work, indicating that specific work is indeed the correct control variable, in agreement with previous findings.3,22,44 We would like to explore the effect of varying applied work on crystallization for our various grades in a way that is disentangled from the effect of varying shear rate. For this purpose, we take advantage of the observation that the effect of shear rate saturates above the saturation shear rate γ̇sat. Therefore, to study the effect of varying applied work alone, we perform FIC experiments with the shear rates all chosen larger than γ̇sat for each grade. Figure 12 presents results for crystallization time versus applied work, for all five commercial iPP grades. All results shown are for shearing temperature 170 °C and crystallization temperature 141 °C, with shear rates for each grade indicated in the legend. Evidently, the different grades show different strengths of flow-induced crystallization. CiPP2 again shows essentially no FIC effect, even at a large shear rate of 31.5 s−1 and W > 30 MPa. CiPP1 shows a strong FIC effect, with the crystallization time reduced by up to a factor of 50. CiPP3, CiPP4, and CiPP5 show intermediate FIC effects. Note that all five samples show a saturation of FIC effects with increasing applied work; beyond a characteristic value Wsat, further increases in applied work have no effect on the crystallization time. In Figure 12, the initial slopes of the crystallization time versus work for CiPP1, CiPP4, and CiPP5 are similar, with a smaller initial slope for CiPP3 and essentially zero initial slope for CiPP2. One property that correlates well with this rank ordering of the initial slopes is the shape and prominence of the high molecular weight tail in the molecular weight distribution (see Figure 5). We may hypothesize that for some reason the onset of FIC for applied work below Wsat is governed by the

prominence of long chains (above 104 kg/mol) in the molecular weight distribution. Our five commercial grades also vary with respect to how much crystallization speeds up for applied work at or above the saturation value Wsat. Remarkably, we find that the crystallization rate at saturation correlates well with the tacticity of the sample, with the least isotactic sample exhibiting the largest speedup in crystallization. Figure 13 shows the results for all

Figure 13. Time to tan δ = 1 at 141 °C (for quiescent crystallization and FIC at saturation) versus tacticity. Tacticity error bars are from analysis of 13C NMR data (see main text).

five commercial iPP grades studied. From left to right in Figure 13, the samples in order of increasing tacticity are CiPP1, CiPP5, CiPP3, CiPP4, and finally CiPP2 at 98.9%. This correlation between tacticity and crystallization rate is surprising, for two reasons. First, in quiescent crystallization, low tacticity has the opposite effect (filled squares in Figure 13), resulting in slower crystallization, as mentioned earlier. In fact, from Figure 13 it appears that tacticity has a stronger influence on FIC than quiescent crystallization. Second, tacticity seems to have a stronger influence on FIC than molecular weight. The molecular weights MW from left to right J


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The isotactic sequence mass distribution is plotted for all five grades in Figure 14. In the figure, the number of monomers n is

converted to the length of a 3 × 1 helical crystalline stem, using the polypropylene helix length of 6.5 Å per helical turn consisting of three monomers.72 For comparison, the typical lamellar thickness h at nominal undercooling (corresponding to a stem length of about 12 nm) is indicated in gray, computed from the “crystallization line” of Tc as a function of 1/h.17 Figure 14 suggests that the maximum speedup from flowinduced crystallization is greater when typical isotactic sequences in a sample are comparable to or shorter than the expected lamellar thickness at the given crystallization temperature (typically Tc = 141 °C in our experiments). Still, it is remarkable that CiPP1, with shorter isotactic sequences, crystallizes faster as a result of flow-induced crystallization for applied work at or above saturation than the more isotactic samples (see Figure 13). The saturation value of applied work Wsat has been identified in previous works as an important sample-dependent parameter governing flow-induced crystallization. For applied work in excess of Wsat, crystallization times are constant, which suggests that the number of nuclei formed as a result of FIC reaches a maximum. We would like to know what material properties determine Wsat, which evidently varies among different iPP samples (see Figure 12). The variation of log crystallization time versus applied work in Figure 12 can be represented roughly as a linear decrease to a saturation value. We have observed that the initial slope of this variation seems to correlate with the prominence of the high molecular weight tail, while the maximum speedup appears to correlate with the tacticity of the sample. If these two relations are both valid, the saturation work Wsat would be determined indirectly, by following the initial slope (set by the strength of the high molecular weight tail) down to the minimum crystallization time (set by the sample tacticity). Crystallization Temperature Tc. To this point, we have investigated how shear rate and applied work each affect crystallization time, at a given undercooling. Of course, in quiescent crystallization we know that the degree of undercooling has a strong effect on crystallization time. Now we vary the crystallization temperature Tc to see its effect on the crystallization time as a function of applied work W. Figure 15 displays a family of results for crystallization time versus W, for different values of crystallization temperature Tc. In all these curves, the sample is CiPP1, and the shearing temperature is

Figure 14. Isotactic sequence mass distribution versus stem length, for all five iPP grades. Gray vertical line indicates the 12 nm lamellar thickness at nominal undercooling (130−142 °C).

Figure 15. Crystallization time versus applied work at different crystallization temperatures (see legend) for CiPP1 sheared at 170 °C with shear rate of 2.5 s−1.

in Figure 13 are 445, 475, 254, 462, and 158 kg/mol, but the variation of crystallization time at saturation with tacticity appears smooth with no evident corrections to be made for varying molecular weight. Note also that CiPP1 and CiPP4 have nearly identical molecular weight distributions (see Figure 5) and correspondingly nearly identical linear viscoelastic response (see Figure 4); they differ only in tacticity (95.7% for CiPP1 versus 97.6% for CiPP4, first and fourth points in Figure 13, respectively). The tacticity difference between the two samples appears to account for the striking difference in their flow-induced crystallization response. The modest change in quiescent crystallization times of the five commercial samples in Figure 13 suggests that the variation in concentration of quiescent nuclei is also modest. Assuming that the crystal growth rates in the different samples at the same temperature are similar, faster quiescent crystallization of hightacticity materials implies a higher nucleation rate and hence a higher spherulite number density in the solid sample. But the crystallization times only vary by a factor of about 3 across the tacticity range studied, so the quiescent nucleation densities are similar among the materials. To understand why tacticity should play a key role in flowinduced crystallization, we use 13C NMR data to compute the length distribution of isotactic sequences for each of our iPP grades. Each successive monomer in a polypropylene chain is added either “meso” (on the same side as the previous monomer) or “rac” (on the opposite side). A chain can thus be regarded as a sequence of m and r bonds between successive monomers. 13C NMR reports the fraction of [mm], [mr] + [rm]([mr] = [rm] by symmetry), and [rr] on two successive bonds (see Table 2). The probability per bond p that an isotactic sequence terminates with a “racemic” addition is p = [mr]/([mm] + [mr]), which can be computed for each grade from the NMR data. The normalized mass distribution of isotactic sequences P(n) (probability that a randomly chosen meso addition is on a sequence of length n) is given by P(n) = pn − 1 n(1 − p)2

(7)

K


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Macromolecules held fixed at 170 °C, and the shear rate at 2.5 s−1, above the saturation shear rate. In Figure 15, we see that as the crystallization temperature Tc decreases, the shape of the curve for crystallization time versus work becomes more “bowed out”. The initial slope of the curve is steeper at lower crystallization temperatures, even as the quiescent crystallization time becomes shorter. Thus, the crystallization time becomes more sensitive to small amounts of applied work at lower Tc values. Remarkably, the minimum crystallization time is essentially independent of undercooling, in the range of Tc we studied. This strongly suggests that the minimum crystallization time is due to reaching a maximum nuclei density, driven by both undercooling and specific work. Likewise, the saturation work Wsat remains constant at around 16 MPa for Tc in the range 138−142 °C, consistent with observations of Janeschitz-Kriegl et al.4,40 At the lowest crystallization temperature we studied (Tc = 136 °C), the behavior of the crystallization time versus work changes somewhat, reaching the same minimum time (10 min) at a much lower work (about 4 MPa) and exhibiting some crystallization times at low work levels that are actually slower than at higher crystallization temperatures. This change in behavior may be related to the change in the lamellar growth regime from Hoffman regime II to regime III, which occurs around this temperature.20,60,63 Shearing Temperature Ts. We now turn our attention to the last of the four key process variables, the shearing temperature Ts. Intuitively, we expect that shearing at sufficiently elevated temperatures will have progressively less effect on the subsequent crystallization after quenching because whatever precursors to crystallization may be generated during the shearing will not survive at high temperatures. By varying the temperature at which shear is applied, we can investigate the thermal stability of these flow-induced precursors to crystallization. Figure 16 shows the crystallization time versus shearing temperature Ts over the range 160−240 °C, for sample CiPP1 at nominal conditions with shear rate held constant at γ̇ = 2.5 s−1, a constant applied work of 12.5 MPa, and a constant crystallization temperature Tc = 141 °C. (Our experiments were limited to temperatures above 160 °C because below 160 °C

crystallization proceeds so rapidly that the sample begins to solidify during the shearing, which overwhelms the torque transducer and ends the experiment.) Generally speaking, shearing at lower temperatures results in faster crystallization, as one might expect; but surprisingly, there appear to be three temperature regimes in Figure 16: below about 180 °C, between 180 and 210 °C, and above about 210 °C. The crystallization time appears independent of shearing temperature Ts in the range from about 180 to about 210 °C. For Ts below 180 °C, near or below the spherulite melting temperature (about 170 °C), the crystallization time decreases with decreasing Ts. This could be a result of the combined effect of flow-induced crystallization and lamellar growth during the interval of shear. Chains bridging between growing lamellae (i.e., tie chains) could be further stretched by the flow, leading to an amplification of flow-induced crystallization. For shearing temperatures Ts above 210 °C, the effect of flow-induced crystallization diminishesas Ts increases above 210 °C, the crystallization time steadily rises. This result could be a consequence of the relaxation of whatever shear induced precursors are responsible for the enhanced nucleation that follows the quench after shearing. Perhaps coincidentally, the Hoffman−Weeks temperature, at which the extrapolated crystallization and melting lines cross (discussed in the Introduction), is about 208 °C for polypropylene.73 There may be a connection between the diminished flow-induced crystallization effect at shearing temperatures above 210 °C and the Hoffman−Weeks temperature, sometimes interpreted as the limit of metastability of some as-yet undefined precursor to nucleation. Perhaps as the sample is sheared at these elevated temperatures, the flow-induced precursors to nucleation immediately begin to relax, resulting in a weaker enhancement of nucleation after the subsequent quench to the crystallization temperature. The relaxation of these precursors may proceed more readily at higher temperatures, eventually eliminating the flow-induced crystallization effect. Nonetheless, shearing far above the equilibrium melting temperature (187 °C for polypropylene) remarkably still has an effect on the crystallization time compared to quiescent conditions, as shown by the dashed line in Figure 16. A linear extrapolation of the log of the crystallization time in Figure 16 to the quiescent limit suggests shearing may still reduce the crystallization time even at temperatures as high as 300 °C.

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CONCLUSIONS We investigated flow-induced crystallization (FIC) of five different commercial linear polypropylene samples, with different molecular weight distributions and tacticities. Our samples are all polydisperse (with MW/MN from 3.7 to 7.2), with MW from 158 to 474 kg/mol and with isotactic content from 95.7 to 98.9%. We verify that our samples consist of linear chains by comparing dynamic rheology to tube model predictions based on measured molecular weight distributions. Our purpose in studying PP grades with different material properties is to understand which material parameters govern the magnitude of FIC effects. Using a rheometer, we studied how flow-induced crystallization kinetics vary with four basic processing parameters: shear rate, specific work, crystallization temperature, and shearing temperature. For all samples studied, we find that the crystallization rate increases with shear rate up to a saturation shear rate γ̇sat of

Figure 16. Crystallization time versus shearing temperature, for CiPP1 with shear rate γ̇ = 2.5 s−1 (above saturation), applied work of 12.5 MPa, and crystallization temperature Tc = 141 °C. Dashed line indicates quiescent crystallization time at Tc = 141 °C. L


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about 1 s−1. At this shear rate, only a very small minority of the longest chains (above 104 kg/mol), mass fraction of ∼10−3, have Rouse times long enough to be stretched by the flow. Further increases in shear rate above γ̇sat have no effect on the crystallization rate. The prevailing hypothesis for FIC effects is that chains stretched by the flow are potent in reducing the nucleation barrier. Under this hypothesis, further increases in shear rate should stretch more chains and further speed crystallization. The appearance of a saturation shear rate is not explained by this hypothesis and suggests that somehow chains must be above a certain molecular weight to be effective in FIC, regardless of the shear rate. Similarly, the crystallization rate is observed to increase with specific work W, up to a saturation value Wsat beyond which the crystallization rate remains constant. The influence of work on flow-induced crystallization appears to be stronger for iPP grades with a more pronounced high molecular weight tail, in agreement with previous reports.6,31,37 For all five samples, the magnitude of flow-induced speedup of crystallization at saturation (i.e., for sufficiently large shear rate and applied work) correlates with the tacticity of the sample. Remarkably, chains with lower tacticity show faster crystallization rates at saturation. This trend is opposite to quiescent crystallization, for which higher tacticity samples crystallize faster (see Figure 13). For the samples we studied, tacticity has a much stronger influence on the magnitude of FIC at saturation than differences in molecular weight distribution. We varied the crystallization temperature Tc (to which we quench after shearing) from 142 down to 136 °C. Lower crystallization temperatures speed flow-induced crystallization, in much the same way as quiescent crystallization is accelerated by greater undercooling. Remarkably, the saturation work Wsat appears to be rather insensitive to Tc over the range of temperatures we studied. We varied the shearing temperature Ts (at which shear is applied, before quenching to Tc) over a wide range, from 160 to 240 °C. Flow-induced crystallization persists even when shear is applied well above the equilibrium extended-chain melting temperature (about 187 °C). This observation suggests the flow-induced precursors either are not crystalline or are stabilized somehow by particulate impurities in the samples, because otherwise they would not be expected to survive at such high temperatures. FIC effects finally weaken when shear is applied above the Hoffman−Weeks temperature (about 210 °C), perhaps because flow-induced precursors are no longer metastable.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (S.T.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge support from the National Science Foundation (NSF CBET-1067554). We thank Mike Chung for providing some of the materials studied in this work and Thomas Sun and Willem de Groot for help with sample characterization by gel permeation chromatography. M


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